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Título:
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Dimensionality reduction when data are density functions
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Autor/a:
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Delicado Useros, Pedro Francisco
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Otros autores:
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Universitat Politècnica de Catalunya. Departament d'Estadística i Investigació Operativa; Universitat Politècnica de Catalunya. GREMA - Grup de Recerca en Estadística Matemàtica i les seves Aplicacions |
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Abstract:
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Functional Data Analysis deals with samples where a whole function is observed for each
individual. A relevant case of FDA is when the observed functions are density functions.
Among the particular characteristics of density functions, the most of the fact that they are an example of infinite dimensional compositional data (parts of some whole which
only carry relative information) is made. Several dimensionality reduction methods for
this particular type of data are compared: functional principal components analysis with or without a previous data transformation, and multidimensional scaling for different interdensity distances, one of them taking into account the compositional nature of density functions. The emphasis is on the steps previous and posterior to the application of a particular dimensionality reduction method: care must be taken in choosing the right density function transformation and/or the appropriate distance between densities before performing
dimensionality reduction; subsequently the graphical representation of dimensionality
reduction results must take into account that the observed objects are density
functions. The different methods are applied1 to artificial and real data (population pyramids for 223 countries in year 2000). As a global conclusion, the use of multidimensional scaling based on compositional distance is recommended. |
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Materia(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
-Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica
-Numerical analysis
-Mathematical statistics
-Compositional data
Functional data analysis
Graphical output
Kullback-Leibler divergence
Lp distance
Multidimensional scaling
Population pyramids
Principal components analysis
-Estadística matemàtica
-Anàlisi global (Matemàtica)
-Classificació AMS::65 Numerical analysis
-Classificació AMS::65 Numerical analysis |
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Derechos:
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Tipo de documento:
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Artículo - Versión publicada
Artículo |
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